Communications and Control for Electric Power Systems ...

JPL Publication 94-8

Communications and Control

for Electric Power Systems:

Power System Stability Applicationsof Artificial Neural Networks

N. Toomarian

H. Kirkham

April 1994

Prepared for

Office of Energy Management SystemsUnited States Department of Energy

Through an agreement with

National Aeronautics and

Space Administration

by

Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California

Prepared by the Jet Propulsion Laboratory, California Institute of Technology,for the U.S. Department of Energy through an agreement with the National

Aeronautics and Space Administration.

This report was prepared as an account of work sponsored by an

agency of the United States Government. Neither the United States Governmentnor any agency thereof, nor any of their employees, makes any warranty,

express or implied, or assumes any legal liability or responsibility for the

accuracy, completeness, or usefulness of any information, apparatus, product,

or process disclosed, or represents that its use would not infringe privately

owned rights.Reference herein to any specific commercial product, process, or

service by trade name, trademark, manufacturer, or otherwise, does not

necessarily constitute or imply its endorsement, recommendation, or favoringby the United States Government or any agency thereof.

This publication reports on work performed under NASA Task RE-152,

Amendment 203 and sponsored through DOE/NASA Interagency AgreementNo. DE-AI01-79ET 29372 (Mod. A009).

ABSTRACT

HIS REPORT investigates the application of artificial neural networks to the problem ofpower system stability. The field of artificial intelligence, expert systems and neural

networks is reviewed. Power system operation is discussed with emphasis on stability consider-

ations. Real-time system control has only recently been considered as applicable to stability,

using conventional control methods. The report considers the use of artificial neural networks

to improve the stability of the power system. The networks are considered as adjuncts and as

replacements for existing controllers. The optimal kind of network to use as an adjunct to a

generator exciter is discussed.

iii

FOREWORD

HIS REPORT discusses the application of the relatively new technology of artificial neuralnetworks to one of the oldest problems of electric power systems: stability. Power systems

are nonlinear in certain respects, and that means that instability of various kinds is possible. The

instability considered in this report is the kind demonstrated in the New York blackout of 1965.

While the problem is an old one, it is likely to be of increasing importance to find a

solution. A number of evolutionary pressures are acting now so as to change radically the nature

of the industry. These were reviewed at a meeting organized by the Department of Energy

(DOE) in Denver, Colorado, in March 1990. Real-time control and operation were considered

in detail at a DOE Workshop, also in Denver, in November 1991. At the first meeting, the

factors affecting the evolution of the industry were thought to include:

• the regulatory process

• industry competitiveness

• new technologies

• load growth

• renewable sources and storage• environmental concerns.

Because of the first three of these factors, it was estimated that by 2020 over 50 % of new

generation would be non-utility owned, and transmission line loading would be high. These are

the ingredients for trouble. The report of the first Denver meeting concluded that blackouts and

brownouts would occur if existing control devices and operating practices continued to be used.

The work described in this report is aimed at developing new control devices and operat-

ing practices that may contribute to forestalling the difficulties seen for the future power system.

Given the lead-time required to put any new technology into practice, it is not too early to start

investigating such advanced concepts as controllers based on artificial neural networks. Our work

shows that neural nets could be a valuable addition to the options available for power system

operation.

Because we are mixing two disparate technologies, power systems and neural nets, some

background material on both topics is included in this report. The reader who feels the need to

brush up on either topic should find help in Part 1 or Part 2 of the report. The reader who is

comfortable in both areas may skip directly to Part 3.

HAROLD KIRKHAM

PASADENA, CALIFORNIA

APRIL 1994

V

PRC,-4NIE)_Ne PIIGE ltLANK NOT FIRMED

TABLE OF CONTENTS

ABSTRACT ............................................... iii

FOREWORD .............................................. v

PART 1. POWER SYSTEM STABILITY ............................ 1

PART 2: NEURAL NETWORKS ................................. 9

AI Modeling and Neural Networks ............................. 11

A History of Artificial Neural Networks .......................... 13

Computational Neural Learning ............................... 16

Adaptive Neural Control System Architectures ....................... 18

Direct Implementation .................................. 20

Indirect Implementation .................................. 21

Summary .......................................... 22

Neural Hardware Implementation ............................... 23Conclusions ............................................ 26

PART 3. APPLICATION ...................................... 29

Application of Neural Networks ............................... 32

Future Work: Feasibility Study and Network Selection ................. 34

APPENDIX A. NEURAL LEARNING FORMALISM .................... 37

REFERENCES ............................................. 43

vii

__c_ PAGE BLANK NOT FILMED

LIST OF FIGURES

Figure Page

1-1. Simple power system ...................................... 2

1-2. Respecified system ........................................ 3

1-3. Machine and infinite bus .................................... 5

1-4. Power-angle curve ........................................ 7

2-1.

2-2.

2-3.

2-4.

2-5.

2-6.

Model of a neural system .................................... 14

Biological neuron ........................................ 15

Functional model of simulated neuron ............................ 16

Direct adaptive control ..................................... 20

Indirect adaptive control .................................... 22

Computational capabilities of some biological systems .................. 24

3-1.

3-2.

3-3.

3-4.

Simple power system ...................................... 30

Generator controls ........................................ 31

3-machine power system .................................... 32

Power system stabilizer with neural network ........................ 33

A-1. Topology of a general network ................................ 38

.°oVUl

PART 1. POWER SYSTEM STABILITY

tOWER SYSTEM OPERATION is a complex topic. The way energy flows in an inter-connected network is not obvious, and difficult to analyze even in the steady state. The fact

that the system is nonlinear can lead to instability. The objective of maintaining high reliability

of service in spite of these features of the system have led, over the years, to some conservative

ways of operating.

It seems fair to ask why the electric power system presents a problem in determining load

flow. After all, the components of the power system, the lines, transformers and generators, are

all well-understood devices. In part the difficulty stems from the fact that the load on the system

is not known. It can be said that the load is not simply resistive, and is distributed geographical-

ly, but its power demand is not known, or indeed directly measurable. Another part of the

problem arises from the way the system parameters are specified. An example will illustrate the

point.

Consider the simple system shown in Figure 1-1. There are two generators, a single load,

and two resistors representing the losses in the transmission lines. (Although most power systems

are ac, we can demonstrate the analytical difficulties more clearly with a dc system, as shown.)

We begin by specifying that the left generator output is 100 W, and the load power is

150 W at 100 V. (This kind of specification of the generation is reasonably representative of

power system practice. The left generator might be a small efficient unit, running at full power.)

JPL 94-8, page 1

Part 1: PowerSystem Stability

The problem is to determine the bus voltages V s and V3 and the power to be delivered

by the right generator. When these three quantities are known, the system operating conditionswill be known.

Figure 1-1. SSimple power system

11 10 V2= 100V 10 13

Pt2

LOAD

150W

00W

V 3

P

)

The load current is

Two expressions can be written for/1:

/1 =_

and

from which 11 = Vs - 100.

150W -1.5A (1-1)/2- lOOV

100

171 (1-2)

}'1 -V2 (1-3)Is= 1

The voltage VI of the left generator is uniquely specified because

100 =Vx-100vl

or

This may be solved directly

Of course,

By Kirchoff's Current Law,

and we can solve for I3:

(1-4)

V12 - 100V s - 100 =0 (1-5)

V 1 = 100.99V (1-6)

I s = 10---0-0=0.99A (1-7)vl

I2 =I s+I 3 (1-8)

13=12 -11 = 1.50 - 0.99 =0.51 A (1-9)

}'3 can be found by considering the volt-drop due to 13 in the 1 0 line resistance. The

result is V3 = 100.51 V. Now the power from the right generator can be found:

P, = V313 =51.26W (1-10)

JPL 94-8, page 2

Part 1- Power System Stability

The system is now completely analyzed. The right generator must burn enough fuel to

generate 51.26 W, and the field current must be adjusted for a terminal voltage of 100.51 V.

The left generator must supply 100 W at 100.99 V.

Although the system is extremely simple, the above analysis illustrates some important

concepts. In the real world, the exact power of the load is not generally known. In scheduling

the generation, one generator is designated as the "slack" machine (the right hand generator in

the example), characterized by an initially unknown power generation. The power is then

adjusted so that the frequency is at the required value: by definition the demand is then being

met.

The purpose of a load flow calculation such as the one above is to determine the voltages

and power flows throughout the system, based on the measured data. There are 5 degrees of

freedom in the circuit of Figure 1-1. In other words, the specification of five independent

quantities serves to totally determine the behavior of the system. In our example, the five

quantities were the power of the left generator, the power of the load, the load voltage and the

two line resistances. These are not the traditionally specified parameters. The load is

geographically distributed, and is voltage dependent. Load power is therefore not known, butmust be found in a load flow calculation.

The specification of different parameters has a profound effect on the calculation. Let us

solve the system again with the following parameters specified: the power of the left generator,

the two line resistances, the power at the load and the voltage at the right generator. This system

is shown in Figure 1-2.

Figure 1-2. SRespecified system \

I 1_

y°V2

12

LOAD

150W

lt3 13 V3- IOOV

P

We proceed in a straightforward fashion to determine the power to be supplied by the

right generator as well as the two remaining bus voltages 111and V2.

e (1-11)/3--

eV2_- 100- 113 = 100-_ (1-12)

100

P_o_ = V212= 150 (1-13)

2 _

150

[100

JPL 94-8, page 3


[1 =[2 -[3 =150 P

[ 100 - -i-_p] 100 (1-15)

150 P+ - _ (1-16)

[Io0-P] 100

P_. = 100 = 1/'1/_ (1-17)

Substituting for 1"1, 11 in this equation yields one equation involving P that we can use

to determine system operating point. The equation is a fourth order polynomial in P. Numericalevaluation leads to

P=51.25W

The other values follow immediately:

I3 =0.5125A

Vz =99.4875V, I2 =1.5077A

V 1 =100.4827A, I_ =0.9952A

(1-18)

(1-19)

(1-20)

The analytic complexity of the solution is masked by the few lines above indicating that

the equation is a fourth order polynomial in P. Although this second problem appears to be a

minor variation of the first (indeed the final values for the current, voltage and power are not

significantly different), the mathematical complexity is such as to require numerical techniques.

And this is for a system with only five degrees of freedom[ A real power system will have

several thousand degrees of freedom, and will be specified in the way our second example wasspecified. Numerical methods are clearly called for.

We have seen how difficult it is to fix the steady-state operating point of a power system.

Now let us turn to the dynamics of the system.

Once more, we will illustrate the problem by means of an example. Consider another

simple power system, consisting of one machine and an infinite bus 1, connected by two

transmission lines, as shown in Figure 1-3.

z An infinite bus is a hypothetical convenience. It is a connection point defined so that whatever

power is inserted into it (or taken out of it), the frequency and the voltage remain constant. This has the

advantage for our purposes that it makes the equations of motion of the system much simpler. (In

practice, as far as any single generator in a power system is concemed, the remainder of the system looks

very much like an infinite bus. Choosing to use an infinite bus in the following example is not much ofan approximation.)

JPL 94-8, page 4


Figure 1-3.Machineand infinite bus

GENERATORv_

Voo INRNITE

BUS

r-

Note that this diagram uses a different representation for the power system. This

representation is a single line diagram, often used when the concern is more with the flow of

power than the details of the circuit, as we are here. The three-phase lines and buses are shown

simply as lines, and the machines as circles. The square boxes represent circuit breakers.

The voltage at the terminals of the generator is V1, and at the infinite bus is V=. If the

impedance of the two transmission lines is X, the power flow into the infinite bus can be written

P = V x V= sire5 (1-21)X

where b is the angle between the voltage phasors V_ and V=. The angle fi is called the power

angle, because it is this parameter that primarily determines the power transfer, as will be seen

below.

There are a number of simplifications in the preceding development. For instance, it is

assumed that the value of the impedances (lumped together as the transfer impedance X between

the generator and the infinite bus) is constant. In practice, this is not the case. The impedance

includes a component that is due to the generator itself, chiefly the inductance of the generator

windings. This impedance is not constant as the power output of the generator varies, because

the position of the generator rotor with respect to the rotating field of the stator varies. Since

part of the rotor has been machined to accommodate the windings, the inductance is not constant

as a function of position.

Another assumption is that the generator voltage is constant, or rather that the voltage

behind the impedance of the generator is constant. This is only true if there is no automatic

voltage regulator (AVR) on the machine. In practice, AVRs are fitted to all machines, to help

keep the terminal voltage constant. Using a model such as that shown in Figure 1-3, the best

simple approximation would be that V_ is constant.

Nevertheless, the equation for the power transfer illustrates some important points. First,

the power transfer does not depend on the voltage. V= is constant by definition. V_ is practically

constant. The power transfer is primarily a function of the angle d between the voltages at the

two ends of the system.

Second, the power transfer is inversely proportional to the transfer impedance. If the

impedance X is due to two identical lines of impedance 2X, the loss of one line would instantly

halve the power transfer. More about this in a moment.

Third, the power transfer has a maximum value given by (V_ V_)/X. If the voltage

magnitudes are nominal, or 1 per unit, the maximum power transfer is simply 1/X, and occurs

when c5equals 90".

It is this sinusoidal dependence on _ and the existence of a maximum value for the power

transfer that makes the system capable of becoming unstable. Suppose that the machine is

operated so that fi = 45 o when one of the transmission lines is tripped out. If the two lines are

JPL 94-8, page 5


identical, there will be a problem. Before the line is tripped we have

etransfer = V1V2 sin45°

X (1-22)0.707

X

In other words, the power transfer is approximately 70% of its maximum value for the

system. After the line is removed, the maximum possible power transfer is halved. The

generator finds that it is operating with too low a value of _5to transfer the input power. The

excess power goes into accelerating the machine, which serves to increase c5.

In this particular case, when 6 reaches 90 ° there is still an excess of input power over

power transferred, and the machine continues to accelerate. The post-fault value of maximum

power transfer is half the pre-fault value, and the input power is 70 % of the pre-fault value, or

140% of the post-fault maximum. The machine continues accelerating indefinitely, and will

eventually be tripped out. This kind of instability is called steady-state instability, because there

is no steady-state solution to the problem.

The usual answer to this kind of problem is to avoid it by operating with a smaller power

angle. This is a very conservative approach, and it means that equipment is being under-utilized.

Of course, as the transmission system becomes more interconnected, the loss of a single line

would not mean a doubling of the transfer impedance, so larger values of power angle can safely

be used. However, there are still many instances where standard practice is to keep power angles

at less than 30 ° during normal operation. In such a case, the stability question is determined by

the dynamics of the system. The question of what is called transient stability arises.

We said above that the machine would accelerate when it was being driven with more

power than was being transferred out electrically. The equation of motion is

Md2----_+ Pm_xsin 6 = P (1-23)at 2 ou,

where M is the inertia constant of the machine, and Pr_x is the maximum power that could be

transferred, VIV2/X. If _ is constant, the first term vanishes and the equation restates the

sinusoidal nature of the power transfer equation. When the value of c5is changing, the motion

is similar to that of a pendulum, governed by a second-order nonlinear equation. The equation

of motion is called the swing equation.

Note that there is no first order term in the swing equation. This means that the motion

is undamped. Once an oscillation is started, there is nothing to prevent its continuing

indefinitely. This is because the resistance terms in the power system (line losses and the like)

are negligible in effect. In the derivation of the swing equation (which can be found in the text

books, for example Stevenson, 1962; Elgerd, 1971), the resistances are explicitly ignored. In

practical terms, this is a good, perhaps conservative, approximation. In a large, interconnected

system with many generators, there are so many other factors that can affect the motion of a

generator (particularly exciter control systems) that the damping is usually very small.

Suppose that, for some unspecified reason, one line in the system of Figure 1-3 trips out.

In terms of the power-angle curves, the result is as shown in Figure 1-4.

JPL 94-8, page 6

Part 1: Power System Stability

Figure 1-4.Power-anglecurve

D-

1

0.8

0.6

0.4

0.2

0

.0.2

-0.4

a& _2 90° _.

Before the fault, the system is operating with power angle 3_. After the line has tripped,

operation at the same power level (about 0.4 per unit) could resume at power angle c52,as shown

by the dotted line. However, the system trajectory is actually as shown by the heavy line in

Figure 1-4. At first, the power angle does not change. The power decreases (to less than 0.2 per

unit). The excess input power accelerates the machine, and the power angle increases towards

32.

Although the heavy line in Figure 1-4 stops at 32, in practice the momentum of the

system will cause an overshoot beyond the new steady-state operating point. If the power angle

increases beyond 90 °, further increases in power angle will result in a decrease in power

transferred, and the system will be unstable. This could happen because of the overshoot. The

system shown would exhibit transient instability. It is precisely this kind of instability that the

application of artificial neural nets, described in the third part of this report, is designed to

prevent.

There are several simplifying assumptions behind this discussion. Most importantly, it

has been assumed that the excitation is constant. If, instead, the excitation is made a function

of the power angle, the power angle curve can be modified so that increased power can be

transferred, at the cost of increasing the voltage in the system. In the real world, a generator is

usually connected to an interconnected network of other machines, and there is no single value

of 3. The excitation may be varied according to a locally available measurement, such as the

derivative of the machine speed. This has the effect of adding a derivative term to the equation

of motion, and improving the stability by adding damping. (It may also have the unwanted effect

of resonating with system parameters, but that need not concern us here.) The device that is used

to modulate the excitation for this purpose is termed a power system stabilizer.

The use of an artificial neural network as an adjunct to or a replacement for a power

system stabilizer to modulate the excitation is the subject of the third section of this report. In

the next section, we introduce the topic of artificial neural networks, as background for this

application.

JPL 94-8, page 7

PART 2" NEURAL NETWORKS

HE QUEST for efficient computational approaches to artificial intelligence (AI) hasundergone a significant evolution in the last few years. Attention has come to focus on the

application of neural learning concepts to some of the many tasks performed by machines. This

must be complemented by some insight into how to combine symbolic reasoning with massively

parallel processing abilities. Computer scientists seek to understand the computational potential

of this emerging technology. They are interested in knowing the fundamental limitations and

capabilities of handling unstructured problems by intelligent machines. Issues such as this are

central to the deeper question of the feasibility of neural learning vis gt vis artificial intelligence.

The focus of this part of the report is narrower; to examine generally the capabilities of

neural network learning. Machine learning in the context of neural networks is examined from

the standpoints of computational complexity and algorithmic information theory.

Not only is the concept of massively parallel neuroprocessing of scientific interest, it is

also of great practical interest. It is changing the nature of information processing and problem

solving. In general, the scientific and engineering community is faced with two basic categories

of problems. First, there are problems that are clearly defined and deterministic and controllable.

These can be handled by computers employing rigorous, precise logic, algorithms, or production

rules. This class deals with structured problems such as sorting, data processing, and automated

assembly in a controlled workspace. Second, there are scenarios such as maintenance of nuclear

plants, undersea mining, battle management, and repair of space satellites that lead to computa-

JPL 94-8, page 9

p_ PAGE, BL.A,e4K r_iOT FILtd[#

Part 2: Neural Networks

tional problems that are inherently ill-posed. Such unstructured problems present situations that

may have received no prior treatment or thought. Decisions need to be made, based on

information that is incomplete, often ambiguous, and plagued with imperfect or inexact knowl-

edge. These cases involve the handling of large sets of competing constraints that can tolerate

"close enough" solutions. The outcome depends on very many inputs and their statistical

variations, and there is not a clear logical method for arriving at the answer. The focus of

artificial intelligence and machine learning has been to understand and engineer systems that can

address such unstructured computational problems.

Engineered intelligent systems, that is expert systems with some embedded reasoning,

such as might be used for autonomous robots and rovers for space applications, behave with

rigidity when compared to their biological counterparts. Biological systems are able to recognize

objects or speech, to manipulate and adapt in an unstructured environment and to learn from

experience. Engineered systems lack common sense knowledge and reasoning, and knowledge

structures for recognizing complex patterns. They fail to recognize their own limitations and are

insensitive to context. They are likely to give incorrect responses to queries that are outside the

domains for which they are programmed. Algorithmic structuring fails to match biological

computational machinery in taking sensory information and acting on it, especially when the

sensors are bombarded by a range of different, and in some cases competing, stimuli. Biological

machinery is capable of providing satisfactory solutions to such ill-structured problems with

remarkable ease and flexibility.

An important part of any development for unstructured computation today is to

understand how unstructured computations are interpreted, organized, and carried out by

biological systems. The latter exhibit a spontaneous emergent ability that enables them to self-

organize and to adapt their structure and function, z

Technical success in emulating some of the fundamental aspects of human intelligence

has been limited. The limitation lies in the differences between the organization and structuring

of knowledge, the dynamics of biological neuronal circuitry and its emulation using symbolic

processing. For example, it has been said that analogy and reminding guide all our thought

patterns, and that being attuned to vague resemblances is the hallmark of intelligence (Hofstader,

1979; Kanal and Tsao, 1986; Linsker, 1986a,b,c; Winograd, 1976). Thus, it would be naive to

expect that logical manipulation of symbolic descriptions is an adequate tool. Furthermore, there

is strong psychophysical evidence that while the beginner learns through rules, the expert

discards such rules, somehow instead discriminating thousands of patterns, acquired through

experience in his domain of expertise.

It is rapidly becoming evident that many of the unstructured problems can be solved not

2 A comment about the use of the word emergent is in order. The first dictionary definition is usually

emerging, which doesn't help much. Suddenly appearing and arising unexpectedly are lower in the list

of meanings. Almost certainly, the use of emergent in our context derives from the emergent theory ofevolution which holds that completely new organisms or modes of behavior appear during the process

of evolution as a result of unpredictable rearrangements of pre-existing elements. This use carries with

it the notion that the results do not arise from a higher external control, but from the operation of a form

of natural selection. In nature, the process occurs as a result of feedback, strengthening some (biological)neural connections and weakening others during learning. In our application, the natural selectioncorresponds to the adjustment of the weights during the training of the artificial neural network.

JPL 94-8, page 10


with traditional AI techniques, but by "analogy", "subsymbolic" or pattern matching techniques.

Hence, the neural network, a biologically inspired computational and information processing

approach, provides us with an inherently better tool. In the remainder of this report, we present

tutorial material that will function as a background for further work on the application of

artificial neural networks to power system problems. The remainder of this section of the report

concentrates on neural networks. Their application to the control problems of power system

stability is examined in Part 3. A mathematical formalism that can provide an enabling basis for

solving complex problems is reserved for an Appendix.

The problem of interest here is one that has been addressed for the last several decades,

namely, functional synthesis. Specifically, we focus on learning nonlinear mappings to abstract

functional, statistical, logical and spatial invariants from representative examples. However,

before we formally introduce neural networks in the technical core of this report, we present

arguments comparing the suitability of neural networks and formal AI to solving problems in

computational learning.

AI Modeling and Neural Networks

Over the last three decades, AI and neural network researchers have charted the ground in the

areas of pattern recognition, adaptive machine learning, perception and sensory-motor control.

This has provided an assessment of what is difficult and what is easy. Although both disciplines

have similar goals, there is not much overlap between their projected capabilities. The basis of

both approaches may be traced back to hypotheses of Leibniz (1951) and Weiner (1948). They

identified humans as complicated goal-seeking machines, each composed of an "intelligent" brain

and highly redundant motor systems. This machine can detect errors, change course, and adapt

its behavior so that the achievement of goals is more efficient.

Later development of intelligent systems has pursued two distinct schools of thought;

symbolic and neurobiological, or connectionist. AI researchers concentrated on what the brain

did irrespective of how it was accomplished biologically, while the connectionists focussed on

how the brain worked. The following material is written by a connectionist.

Rooted in the "rationalist, reductionist tradition in philosophy," AI assumes there is a

fundamental underlying formal representation and logic that mirrors all primitive objects, actions

and relations. This view of the world has the necessary and sufficient means for general

intelligent action. Newell and Simon (1976), are the most forceful proponents of this approach.

They hypothesized that if such a representation were available, the operations of human

cybernetic machinery could be fully automated and described by mathematical theorems and

formal logic. They believed all knowledge could be formulated into rules. Hence, behavioral

aspects of human reasoning and perception could be emulated by following rules or manipulating

symbols, without regard to the varying interpretations of symbols. Further, in this view, intel-

ligent behavior arises from the amalgamation of symbols in patterns that were not anticipated

when the rules were written. Expert systems are the product of such a line of investigation.

However, as discussed by Reeke and Edelman (in Graubard, 1989), over the years AI

researchers have struggled against fundamental systems engineering issues summarized as

follows :

JPL 94-8, page 11

Part 2: NeuralNetworks

Coding Problem: finding the suitable universal symbol system, ie the ultimate simple

units by which all complex things can be understood;

Category Problem: specifying a sufficient set of rules to define all possible categories and

phenomena that the system might have to recognize;

Procedure Problem: specifying in advance all actions that must be taken for all possible

combinations of input;

Homunculus Problem: This pins the fundamental problem of AI to the old puzzle of

"infinite regress" in a universal symbol system. For example, when a person looks at an

object, say a computer, how is the image of the computer registered in the brain? All

explanations hitherto proposed by AI attribute this process to some "intelligent device"

inside the brain that is in charge of doing the registering. However, the same problem

has to be faced again to explain how the "device" does the registering, and so on ad

infinitum;

Developmental Problem: devising mechanisms that can enable programmed systems to

exist, self-learn, self-organize their structure and function, and self-replicate without

explicit external manipulation, akin to adaptive biological systems;

Nonmonotonic Reasoning Problem: designing rules that can function as retractable

hypotheses, to mitigate the problems that arise when rules get executed without context-

consistency checks.

Since formal AI has not been able to surmount the above problems using logical

reasoning alone, some have suggested recourse to an alternate scientific paradigm--neural

networks. In a radical philosophical departure from AI, the neural network community argues

that logical reasoning is not the foundation on which cognition is based. Instead, cognition is an

emergent behavior that results from observing a sufficient number of regularities in the world 3.

The theoretical underpinnings of this approach lie in biological detail and rigorous mathematical

disciplines such as the theory of dynamical systems and statistical physics. Neural network

theorists attempt to discover and validate the principles that make intelligence possible by

observing existing intelligent systems, ie the brain. They hold the view that cognitive machinery

is built from many simple, nonlinear, interacting elements. These neural networks store

knowledge in their internal states and self-organize in response to their environments. Intelligentbehavior results from collective interactions of these units.

Historically, the symbolic community has treated the human brain as a hierarchical

system of components which obey the laws of physics and chemistry. The system could be

described as one which generates solutions to mathematical equations by deriving computable

functions from the inputs and outputs of neurons. It is assumed that given an initial state and a

3 One might assume from the origin of the word that the emergent behavior is spontaneous in origin,

and indeed this is the case. The inner workings of most networks defy exact comprehension. One shouldnot, however, be too uncomfortable with this. Artificial neural networks are trained, and while the details

of how that training actually functions cannot be precisely predicted, the overall result can be estimated

satisfactorily.

JPL 94-8, page 12


sufficient amount of computing power, one could compute a person's next state. This approach

ignored the framework of interpretation, "context-sensitivity," within which humans processinformation, make commitments and assume responsibility. The primary focus of AI became to

design rule-systems that processed symbols without regard to their meanings. Thus, it completely

ignored the considerable amount of subsymbolic or subconscious processing that precedes our

conscious decision making, and later leads to the filtering of situations so that the appropriate

rule may be used. In sharp contrast, rather than creating logical problem-solving procedures,

neural network researchers use only an informal understanding of the desired behavior to

construct computational architectures that can address the problem. This, it is hoped, willeliminate the fundamental M limitation, lack of context sensitivity.

Whereas formal AI focusses on symbols, symbolic manipulation, or formal logic proce-

dures, neural networks focus on association, units and patterns of activation. Neurocomputation

primarily entails recognizing statistically emergent patterns, and processing alternatives obtained

by relaxing various features that characterize a situation.

Therein lies the performance potential of neural networks. They are amenable to the

development and application of human-made systems that can emulate neuronal information

processing operations. Examples of applications include real-time high-performance pattern

recognition, knowledge-processing for inexact knowledge domains, and precise sensory-motorcontrol of robotic effectors. These are areas that computers and AI machines are not suited for.

Neural networks are ideally suited for tasks where a holistic overview is required, eg to abstract

relatively small amounts of significant information from large data streams, such as in speech

recognition or language identification. On the other hand, digital computers and AI are ideal for

algorithmic, symbolic, logical and high precision numeric operations that neural networks are

not suited for. The two fields complement each other in that they approach the same problems

but from different perspectives.So far, we have tried to describe the application and potential of neural networks. We

now present a brief summary of their evolutionary history.

A History of Artificial Neural Networks

The field of artificial neural networks has been revitalized by recent advances in the following

three areas:

1. our understanding of anatomical and functional architecture; the chemical composition,

electrical and organizational processes occurring in the brain and nervous system;

2. hardware technology and capability, leading to physical realizations of neural networks;

3. new network architectures with collective computational properties such as time sequence

retention, error correction and noise elimination, recognition, and generalization.

Development of detailed models of neural networks began with the work of McCulloch

and Pitts (1943). Using logical elements they demonstrated that synchronous neural nets could

perform all quantifiable processes, eg arithmetic, classification, and application of logical rules.

Hebb (1949) demonstrated that repeated activation of one group of neurons by another through

a particular synapse leads it to activate synchronously groups of neurons to which it is weakly

JPL 94-8, page 13


connected, thereby organizing strongly connected assemblies. Neumann (in Grossberg 1987b),

injected the notion of redundancy in neurocomputing. He constructed networks which activated

many neurons to do the job of one. Winograd and Cowan (1963), extended his work to introduce

the notion of distributed representation. In this representation, each neuron partially represented

many bits. The field was put on a firm mathematical basis by Rosenblatt (1962). He conjectured

that intelligent behavior based on a physical representation was likely to be difficult to formalize.

According to his arguments, it was easier to make assumptions about a physical system and then

investigate the system analytically to determine its behavior, than to describe the behavior and

then design a physical system by techniques of logical synthesis. He engineered his ideas in a

feedforward network of McCulloch and Pitts neurons (1943), named perceptrons. He attempted

to automate the procedure by which his network of neurons learned to discriminate patterns and

respond appropriately. A detailed study of perceptrons led Minsky and Papert (1969) to strong

criticism of the field. Thereafter, neural network receded into a long slump. However, as

observed by Ladd (1985), Minsky was mistaken in interpreting or suggesting that simple

perceptrons were at the heart of connectionism. Their analysis was not valid for systems that

were more complex, including multilayered perceptrons and neurons with feedback.

The resurgence of the field is due to the more recent theoretical contributions by Kohonen

(1977-1987), Grossberg (1987a, 1987b), Amari (1972-1983), Carpenter and Grossberg (1987a,

1987b), Hopfield ( 1982,1984), and Zak (1988-1991). Hopfield's illuminating contributions have

extended the applicability of neural network techniques to the solution of complex combinatorial

optimization problems (Hop field and Tank 1985).

As shown in Fig. 2-1, artificial neural systems may be characterized as distributed

computational systems comprised of many processing units. Each processing element has

connected to it several others in a directed graph of some configuration. They have been defined

(Kohonen, 1988) as

massively parallel, adaptive dynamical systems modeled on the general features ofbiological networks, that can carry out useful information processing by their state

response to initial or continuous input. Such neural systems interact with the objects of

the real world and its statistical characteristics in the same way as biological systems do.

Figure 2-1.Model of a neural system

BASIC ELEMENT

I i

For the hth neuron

[

//: :, ........ ,

i:iiii ::il

U i is the potential, _ activity level

Wii is the synaplJcweight o! Ire connection from

G i' is the firing rate funclJon

I i is the extemal input

K i is a decay constant

itoj

JPL 94-8, page 14


Grossberg (1988) has observed that neural networks must:

(a) be nonlinear

(b) be nonlocal, ie exhibit long-range interactions across a network of locations

(c) be nonstationary, ie interactions are reverberative or iterative

(d) have nonconvex "energy-like" function.

The potential advantages of neuronal processing arise as a result of the network's ability

to perform massively parallel, asynchronous and distributed information processing. Neurons

with simple properties, interacting according to relatively simple rules, can collectively

accomplish complex functions.Neural network modeling is a discipline which attempts to understand brain-like

computational systems. It has been variously termed computational neuroscience, parallel

distributed processing, and connectionism.The bulk of neural network models can be classified into two categories: those that are

intended as computational models of biological nervous systems or neuro-biological models, and

those that are intended as biologically-inspired models of computational devices with

technological applications, called Artificial Neural Systems (ANS).

Although our primary emphasis is on ANS, we will highlight the influence of neurobiolo-

gy on the formulation of ANS models, and the resulting computational implications. To get a

sense of the required size and interconnectivity of neuronal circuitry for intelligent behavior, we

begin by examining biological neural networks. Most existing neural network models are basedon idealizations of the biological neuron and the synaptic conduction mechanisms, shown in

Figure 2-2.

_ CYTON

//

AXON

Figure 2-2. ..... NUCLEUSBiological neuron

DENDRITES AXON TERMINALS

As shown in Fig 2-2, each neuron is characterized by a cell body or cyton and thin branching

extensions called dendrites, that are axons specialized for inter-neuron transmission. The dendrite

is a passive receiving and transmitting agent, whereas the axon is electrochemically charged, a

highly active brain cell entity. The dendrites receive inputs from other neurons (by way of

chemical neurotransmitters), and the axon provides outputs to other neurons. The neuron itself

is imbedded in an aqueous solution of ions, and its selective permeability to these ions (the cell

membrane contains ion channels) establishes a potential gradient responsible for transmitting

information. The electrochemical input signals or the neurotransmitter is funneled to the neuron

from other neurons, to which it is connected through sites on the their surface, called synapses.

The input signals are combined in various ways, triggering the generation of an output

signal by a special region near the cell body. However, the neurobiological phenomenon that is

of particular interest is the changing chemistry of the synapse as information flows from one

JPL 94-8, page 15


neuron to another. The synapse instantaneously decides when the information is not essential and

need not be resupplied. The weight of the individual charge is regarded as the determining

factor. On the transmitting or pre-synaptic side of the synapse, triggering of the synaptic pulse

releases a neurotransmitter that diffuses across a gap to the receiving side of the synapse. On

the post-synaptic or receiving side, the neurotransmitter binds itself to receptor molecules,

thereby affecting the ionic channels and changing the electrochemical potential.

The magnitude of this change is determined by many factors local to the synapse, eg the

amount of neurotransmitter released, and the number of post-synaptic receptors. Therefore,

neurocomputation, biological self-organization, adaptive learning and other mental

phenomena are largely manifested in changes in the effectiveness or "strength" of the

synapses, and their topology. Additional details on the biological neuron, membrane polar-

ization chemistry and synaptic modification may be found in Aleksander (1989).

The above insights in neurobiology have led to the mathematical formulation of simulated

neurons, ie the basic building block of neural network models. A functional model for a typical

simulated neuron is shown in Figure 2-3.EXCITORY

INPUTS_._x_EGRATOR

Figure 2-3. _UTPtrrFunctional model of simulated neuron

INHIBITORYINPUTS

WEIGHTING FACTORS1 THRESHOLD

. "_ OUTPUT

' -' I/_ SUMMER

Four useful areas may be abstracted. The first is the synapse where signals are passed from one

neuron to another, and the amount of signal is regulated, ie gated or weighted by the strength

of the synaptic interconnection. In the activated neuron region, called the summer, synaptic

signals containing excitatory and inhibitory information are combined. This affects the tendency

of a cell to fire or not. The threshold detector actually determines if the neuron is going to fire

or not. The axonal paths conduct the output activation energy to other synapses to which theneuron is connected.

Useful properties such as generalization, classification, association, error correction, and

time sequence retention emerge as collective properties of systems comprised of aggregations

of many such simple units. When viewed individually, the dynamics of each neuron bears little

resemblance to task being performed.

As discussed in the preceding paragraph, of particular computational and modeling

interest are the mathematical notions of synapse and synaptic modification. Further attention is

paid to mechanisms by which such units can be connected together to compute, and the rules

whereby such interconnected systems could be made to learn.

Computational Neural Learning

The strength of neural networks for potential applications arises from their spontaneous

(emergent) ability to achieve functional synthesis. That is to say, they learn nonlinear mappings,

and abstract the spatial, functional or temporal invariances of these mappings. Relationships

between multiple inputs and outputs can be established, based on a presentation of many

JPL 94-8, page 16


representative examples. Once the underlying invariances have been learned and encoded in the

topology and strengths of the synaptic interconnections, the neural network can generalize to

solve arbitrary problem instances. Applications which require solving intractable computational

problems or adaptive modeling are of special interest.

Neural Learning has been defined as the process of adaptively evolving the internal

parameters, eg connection weights and network topology, in response to stimuli (representative

examples) being presented at the input (and possibly at the output) buffer. Neural networks

modeled as adaptive dynamical systems rely on relaxation methods rather than a heuristic

approach for automatic learning.

Learning in neural networks may be supervised. In this case, the desired output response

to the input stimuli patterns is obtained from a knowledgeable teacher. The network is presented

repeatedly with training patterns, and detects the statistical regularities embedded within them.

It learns to exploit these regularities to draw conclusions when presented with a portion or a

distorted version of the original pattern. The retrieval process involves presentation of one of

the stimuli patterns to the network and comparison of the network response to the desired one.

When a portion of a training pattern is used as a retrieval cue, the learned process is called auto-

associative. When the presented input is different from any input presented during training, the

learning is called hetero-associative.

When no desired output is shown to the network the learning is unsupervised. This kind

of learning is relevant to grouping or clustering. For instance, let us assume that the network

is presented with 10 different pictures of two different individuals. After training, the network

will have three states, ie, individual A, B or not known. When the network is presented with

one of the ten pictures, or one sufficiently close to one of them, it should converge to A or B.

On the other hand, presenting a totally new picture to the network may result in convergence

to any of the three states. However, to train the network on labeling the states is a task for

supervised learning.

An intermediate kind of learning is reinforcement learning. Here, a teacher indicates

whether the response to an input is good or bad, how far and in what direction the output differs

from the desired output. The network is rewarded or penalized depending on the action it takes

in response to each presented stimulus. The network configures itself to maximize the reward

that it receives. To illustrate the point, let us take the analogy of a driver trying to park a car

with the assistance of an outside person. In this case, the assistant, playing the role of the

teacher, will give only directions such as, left, more to the left, straight, etc. The teacher does

not have the means to give quantitative value such as 20 degrees to the right. Once the training

is done, the driver should be able to park the car without any assistant.

Along with the architecture, learning rules form the basis of categorizing different neural

network models. A detailed description of different types of learning rules can be found in

Lippmann (1987). Neural learning rules could take the following forms:

Correlational Learning, where parameter changes occur on the basis of local or global

information available to a single neuron. A good example is the Hebbian learning rule

(Hebb, 1949), in which the connection weights are adjusted according to a correlationbetween the states of two interconnected neurons. If the two neurons were both active

during some successful behavior, the connection would be strengthened to express the

positive correlation between them.

JPL 94-8, page 17


On the other hand, in Error-corrected Learning, the rules work by comparing the

response to a given input pattern with the desired response. Weights modifications are

calculated in the direction of decreasing error. Examples are the perceptron learning rule,

and back-propagation. In this category, two methods are available for updating the

weights: (a) add up the weight change due to all stimuli patterns and make an average,

or (b) apply the weight changes due to each stimulus as they are computed. In principle,the two methods should converge into the same end results. However, simulation results

indicate that the first approach is faster.

Another learning rule, Reinforcement Learning, does not require a measure of the desired

responses, either at the level of a single neuron or at the level of a network. A measure

of the adequacy of the emitted response suffices. This reinforcement measure is used to

guide the search process to maximize reward.

Another category is Stochastic Learning, where the network's neurons influence each

other through stochastic relaxation, eg, Boltzmann Machine. In this method, learning

takes place in two stages. First, the network is run with both the input and output

neurons clamped (ie, the value of the input and output neurons set to desired values). Co-

occurrency probabilities are calculated after the network has reached a global minimum.

This procedure is repeated with only the input neurons clamped. Synaptic weights arethen adjusted according to gradient-descent direction.

Two important parameters that characterize the computational power of neural learning

formalisms are the nature of the states of individual neurons, and the temporal nature of synaptic

updating. The states of individual neurons may be either discrete or continuous. It has been

shown that a network with a finite number of states is computationaUy equivalent to a finite statemachine.

Further, the nature of the time variable in neural computation may also be either discrete

or continuous. In the discrete case, the dynamics can be modeled by difference approximations

to differential equations. It has been shown that continuous time networks can resolve temporal

behavior which is transparent in networks operating in discrete time. In all respects, the two

classes are computationally equivalent.

Adaptive Neural Control System Architectures

In a fundamental sense, the control design problem is to find an appropriate functional mapping,

from measured and desired plant outputs, to a control action that will produce satisfactory

behavior in the closed-loop system. In other words, the problem is to choose a function (a

control law) that achieves certain performance objectives when applied to the open-loop system.

In turn, the solution to this problem may involve other mappings, eg from the current plant

operating condition to the parameters of a controller or local plant model, or from measured

plant outputs to estimated plant state. Accordingly, a learning system that could be used to

synthesize such mappings on-line would be an advantageous component of an intelligent control

system. To successfully employ learning systems in this manner, one must have an effective

means for their implementation and incorporation into the overall control system architecture.

JPL 94-8, page 18


Neurocontrol is defined as the use of well-specified neural networks to emit actual control

signals. In the last few years, hundreds of papers have been published on neurocontrol, but

virtually all of them are still based on five basic design approaches:

. Supervised control, where neural nets are trained on a database that contains the

"correct" control signals to use in sample situations;

. Direct inverse control, where neural nets directly learn the mapping from desired

trajectories to the control signals which yield these trajectories;

. Neural adaptive control, where neural nets are used instead of linear mappings in

standard adaptive control;

. The backpropagation of performance, which maximizes some measure of performance

over time, but cannot efficiently account for noise and cannot provide real-time learning

for very large problems;

. Adaptive critic methods, which may be defined as methods that approximate dynamic

programming (ie, approximate optimal control over time in noisy, nonlinear environ-

ments).

Based upon preliminary studies, it is clear that methods 1, 2, and 4 are not well suited

to solve the problem at hand. At this stage, it also seems that both methods 3 and 5 are capable

of solving the problem. However, an in-depth study is needed to demonstrate the superiority of

one over the other. Since the neural adaptive control methodology has the advantage of being

implemented in a straightforward manner, ie as an add-on to the existing adaptive controller, its

implementation and performance will be investigated and analyzed first.

Having discussed the basic features of neural learning systems for control, we will briefly

describe hybrid control system architectures that exhibit both adaptive and learning behaviors.

These hybrid structures incorporate adaptation and learning in a synergistic manner. In such

schemes, an adaptive system is coupled with a neural learning system to provide real-time

adaptation to novel situations and time-varying dynamics. The adaptive control system reacts to

discrepancies between the desired and observed behaviors of the plant, to maintain the requisite

closed-loop system performance. These discrepancies may arise from time-varying dynamics,

disturbances or unmodeled dynamics. The phenomena of time-varying dynamics and disturbances

are usually handled through feedback in the adaptive system. In contrast, the effects of some

unmodeled dynamics can be predicted from previous experience. This is the task given to the

learning system. Initially, all unmodeled behavior is handled by the adaptive system; eventually

however, the learning system is able to anticipate previously experienced, yet initially

unmodeled behavior. Thus, the adaptive system can concentrate on novel situations (where little

or no learning has occurred) and time-varying behavior.

In the following, two general hybrid architectures are outlined. The discussion of these

architectures parallels the usual presentation of direct and indirect adaptive control strategies.

In each approach, the learning system is used to alleviate the burden on the adaptive controller

of continually reacting to predictable state-space dependencies in the dynamical behavior of the

plant. Note that various technical issues must be addressed to guarantee the successful

implementation of these approaches. For example, to ensure both the stability and robustness of

the closed-loop system (which includes both the adaptive and learning systems, as well as the

JPL 94-8, page 19


plant), one must address issues related to controllability and observability; the effects of noise,

disturbances, model-order errors, and other uncertainties; parameter convergence, sufficiency

of excitation, and nonstationarity; computational requirements, time-delays, and the effects of

finite precision arithmetic. Many (if not all) of these issues arise in the implementation of

traditional adaptive control systems; as such, there are some existing sources one may refer to

in the hope of addressing these issues. Although these topics are well beyond the scope of this

document, in some instances, the learning-augmented approach appears to offer operational

advantages over the corresponding adaptive approach (with respect to such implementation

issues). For example, a typical adaptive system would require persistent excitation to ensure the

generation of accurate control or model parameters, under varying plant-operating conditions.

A learning system, however, would only require sufficient excitation, during some training

phase, to allow the stationary, state-space dependencies of the parameters to be captured.

Direct Implementation

In the typical direct adaptive control approach, see Figure 2-4, each control action u is generated

based on the measured Ym and desired ya plant outputs, internal state of the controller, and

estimates of the pertinent control law parameters k. The estimates of the control law parameters

are adjusted, at each time-step, based on the error e between the measured plant outputs and the

outputs of a reference system y,. Of course, care must be taken to ensure that the plant is

actually capable of attaining the performance specified by the selected reference system. Direct

adaptive control approaches do not rely upon an explicit plant model, and thus avoid the needto perform on-line system identification.

Figure 2-4.Direct adaptive control

Yd

The controller in Figure 2-4 is structured so that normal adaptive operation would result if the

learning system were not implemented. The reference represents the desired behavior for the

augmented plant (controller plus plant), while the adaptive mechanism is used to transform the

JPL 94-8, page 20


reference error directly into a correction, zik for the current control system parameters. The

adaptation algorithm can be developed and implemented in several different ways (eg, via

gradient or Lyapunov-based techniques. Learning augmentation can be accomplished by using

the learning system to store the required control system parameters as a function of the operating

condition of the plant. Alternatively, learning can be used to store the appropriate control action

as a function of the actual and desired plant outputs. The schematic architecture in Figure 2-4shows the first case.

When the learning system is used to store the control system parameters as a function of

the plant operating condition, the adaptive system would provide any required perturbation to

the control parameters k generated by the learning system. The signal from the control block

to the learning system in Figure 2-4 is the perturbation in the control parameters 6k to be

associated with the previous operating condition. This association (incremental learning) process

is used to combine the estimate from the adaptive system with the control parameters that have

already been learned for that operating condition. At each sampling instant, the learning system

generates an estimate of the control system parameters k associated with that operating

condition, and then passes this estimate to the controller, where it is combined with the

perturbation parameter estimates maintained by the adaptive system and used to generate the

control action u. In the ideal limit where perfect learning has occurred, and there is an absence

of noise, disturbances, and time-varying dynamics, the correct parameter values would always

be supplied by the learning system, so that both the perturbations 6k and corrections zlk

generated by the adaptive system would become zero. Under more realistic assumptions, there

would be some small degradation in performance because of adaptation (eg, tSk and zik might

not be zero because of noise).

In the case where the learning system is trained to store control action directly as a

function of the actual and desired operating conditions of the plant, the adaptive system would

provide any required perturbation to the control action generated by the learning system. Note

that a dynamic mapping would have to be synthesized by the learning system if a dynamic

feedback law were desired (which was not necessary in the first case). The advantage of this

approach over the previous one is that a more general control law can be learned. The

disadvantage is that additional memory is required and that a more difficult learning problemmust be addressed.

Indirect Implementation

In the typical indirect adaptive control approach, see Figure 2-5, each control action u is

generated based on the measured Ym and Ya desired plant outputs, internal state of the controller,

and estimated parameters Pa of a local plant model. The parameters k for a local control law are

explicitly designed on-line, based on the observed plant behavior. If the behavior of the plant

changes (eg, because of nonlinearity), an estimator automatically updates its model of the plant

as quickly as possible, based on the information available from the (generally noisy) output

measurements. The indirect approach has the important advantage that powerful design methods

(including optimal control techniques) may potentially be used on-line. Note, however, that

computational requirements are usually greater for indirect approaches, since both model

identification and control law design are performed on-line.

JPL 94-8, page 21

Part2: Neural Networks

Figure 2-5.Indirect adaptive control

klICONT.OLI

I=_NIN_:

Ym

If the learning system in Figure 2-5 were not implemented, then this structure would represent

the operation of a traditional indirect adaptive control system. The signal p= is the adaptiveestimate of the plant model parameters. This signal is used to calculate the control law

parameters k. Incorporation of the learning system would allow the plant model parameters to

be learned as a function of the plant operating condition. The model parameters generated by

the learning system allow previously experienced plant behavior to be anticipated, leading to

improved control law design. In this case, the output of the learning system Pl to both the control

design block and the estimator is an a priori estimate of the model parameters associated with

the current operating condition. And a posteriori parameter estimate Pp_t from the estimator

(involving both filtering and posterior smoothing) is used to update the mapping stored by the

learning system. The system uses model parameter estimates from both the adaptive and learning

systems to execute the control law design and determine the appropriate control law parameters.

In situations where the design procedure is complex and time-consuming, the control law

parameters might also be stored (via a separate mapping in the learning system) as a function

of the plant operating condition. Thus, control law design could be performed at a lower rate,

assuming that the control parameter mapping maintained by the learning system was sufficiently

accurate to provide reasonable control in lieu of design at a higher rate.

Summary

In both of the hybrid implementations described in this section, the learning system (prior to any

on-line interaction) would only contain knowledge derived from the design model. During initial

closed-loop operation, the adaptive system would be used to accommodate any inadequacies in

the a priori design knowledge. Subsequently, as experience with the actual plant was ac-

cumulated, the learning system would be used to anticipate the appropriate control or model

parameters as a function of the current plant operating condition. The adaptive system would

remain active to handle novel situations and limitations of the learning system (eg, finite

accuracy). With perfect learning, but no noise, disturbances, or time-varying behavior in the

plant, the contribution from the adaptive system would eventually become zero. In the presence

JPL 94-8, page 22


of noise and disturbances, the contribution from the adaptive system would become small, but

nonzero, depending on the hybrid scheme used. However, the effect of this contribution might

be negligible. In the general case involving all of these effects, the hybrid control system should

perform better than either subsystem individually. It can be seen that adaptation and leaming are

complementary behaviors, and that they can be used simultaneously (for purposes of automatic

control) in a synergistic fashion.

Neural Hardware Implementation

Even to date, a majority of the work in the field of artificial neural networks consists of theory,

modeling, and software simulations of the massively parallel architectures on conventional digital

computers. However, to realize the promise of a high speed, inherently parallel neural network,

architectures must be implemented in parallel hardware. This way, many neurons can actually

communicate and orchestrate their activities simultaneously.

The basic components of electronic neural net hardware are conceptually and functionally

extremely simple. The neurons can be implemented as thresholding nonlinear amplifiers and the

synapses as variable resistive connections between them. An artificial neural network therefore,

consists of many simple processing elements, representing neurons, which interact among

themselves through networks of weighted connections functioning as synapses. The computation

performed by the network is determined by the synaptic weights or connection strengths. The

state of the system is identified by the pattern of activity of the neurons. Given an initial activity

pattern, each neuron receives input signals from the neurons and adjusts its output accordingly

over time. The system rapidly evolves into steady activity pattern which is then interpreted as

a memory recall or as a solution to a problem.

As might be expected, the field of neural networks has developed its own computational

terms. Some understanding of these terms is necessary to appreciate neural network simulation

and implementation requirements. Some of the key concepts and terms are:

A typical neural network contains many more interconnects than neurons, or processingelements.

• Each interconnect requires one multiply/accumulate operation for summing.

Digital computers are normally assessed in terms of storage or memory (where the unit

of measure is words) and speed (instructions-per-second or floating-point-operations-per-

second). The field of neural network defines storage as the value of the input weights and

measures it by the interconnects-per-second within a layer or between layers. (This way

of conceiving neural network storage is important only in the case of network simulation;

in the case of implementation in special-purpose hardware, storage would be handled by

resistive networks and would be defined differently.)

To understand this vernacular and its implications, we will use the terms interconnects

and interconnects-per-second to chart a set of coordinates. We will place interconnects on the

horizontal axis and interconnects-per-second on the vertical axis, respectively. The environment

defined by this chart will be used to describe the computational capabilities of neural network

systems and applications.

JPL 94-8, page 23


To fix the idea, let us introduce the computational capabilities of certain biological

systems, as can be seen in Figure 2-6.

t_

==oo

.=_v

¢-_LIIWO.Ct)

Figure 2-6.Computational capabilitiesof some biological systems

10_6-

10t 4-

1012 -

aplysia•101°

• fly108

106

. leech • worm

104102 ii, lO4 '106 ' 10' 1()1°

STORAGE (interconnects)

human•

10TM 1()14

• bee• cockroach

A human, with the staggering capacity of 1014 interconnects and 1016 interconnects per second,

can be viewed as a superpower compared to creatures such as the worm, the fly, and the bee.

In this context, neural network researchers would be very pleased to be able to replicate the

computational capabilities of a fly or a bee with a machine. However, that will be difficult with

the tools presently available. Today's neural network researchers have access to a variety of

digital tools, that range from low-priced microprocessor-based workstations, through attached

processors and bus-oriented processors, to the more expensive massively-parallel machines, and

finally to supercomputers.

Generally, the micro/minicomputers provide a very modest interconnects-per-second

capability, though in some cases storage capacity is substantial. The speed of these devices is

limiting; neural network models take a very long time to run on them. Attached processors

improve this situation somewhat, since they can boost interconnects-per-second into the millions

from the hundreds of thousands. Bus-oriented processors, in some cases, raise by an order of

magnitude the number of interconnects-per-second available, but storage is not equivalently

greater. The massively parallel systems feature no better speed, and there remain gaps between

their speed and storage capabilities. Supercomputers, meanwhile, do not offer significantly more

capability than systems which cost far less. In addition, the programming necessary to run neural

network models on these massively parallel machines is very complex. It is, in fact, a problem

which limits the extent to which these systems can be used to conduct neural network research.

Moreover, the architectural limitations of these systems prevent researchers from stacking up

several of them to significantly boost their storage or speed.

The present state of neural hardware, in the context of interconnects (storage) and

interconnects-per-second (speed), may satisfy small size simulations. However, it is not very

user-friendly for research, statistical work, or development of large databases. Nevertheless,

several technologies are poised to push hardware capabilities beyond their present speed and

storage limits:

Gallium arsenide (GaAs) and special-purpose charge-coupled devices (CCDs) will push

up the ceiling on interconnects-per-second.

JPL 94-8, page 24

Part2: Neural Networks

Continued developments in random-access memory (RAM) technology as well as the

lesser-developed three-dimensional (3-D) chip technology are expected to expand current

storage capacities.

Multiprocessing, meanwhile, will allow the boundaries of simulation to be moved upward

by an order of magnitude.

Certainly, if neural networks are to offer solutions to important problems, those solutions

must be implemented in a form that exploits the physical advantages offered by neural networks.

The advantages include high throughput that results from massive parallelism (realtime

operation), small size, and low power consumption. In the near term, smaller neural networks

may be digitally implemented using conventional integrated circuit techniques. However, in the

longer term, implementation of neural networks will have to rely on new technologies.

Currently, the development of neural hardware is focussed on the following three major areas:

Direct VLSI/VHSIC (very large scale integration/very high speed integrated circuits). A

mature technology limited to a low density of interconnects due to its two-dimensional

nature. All the weights in a neural network implemented in direct VLSI/VHSIC would

have to be stored in memory, which would require a lot of capacity.

Analog VLSI, which holds promise for a near-term solution. It is two-dimensional, and

offers a high density of interconnects. This is accomplished because the weights can be

implemented in resistors, thereby obviating the need for additional memory.

Optical technology, less developed and longer-term than the silicon-based approaches and

limited in the types of neural networks that it can implement. This offers a very high

density of interconnects due to its three-dimensional nature.

Table 1 summarizes the state of the art neural hardware currently available or under

development. New chips such as these are needed, not only to build neural network simulators,

but also because they may become very valuable individually in neural network-based

applications.

The fabrication and investigation of neural network architectures with different levels of

complexity and various sizes is currently the subject of research. Our approach here at JPL

involves development of fully parallel, cascadable "building blocks". This effort has already

resulted in neural hardware such as fully programmable synaptic interconnection arrays and

nonlinear analog (variable gain sigmoid) neuron arrays. The modular building blocks have served

very well as flexible and versatile research tools. These tools have been employed in the study

of the emergent properties of neural networks. They also provided a sound baseline and

guidelines for the design and implementation of application-specific, high performance

"neuroprocessors". Such neural hardware has successfully been used for solution of real-life

problems, not only at JPL, but also at several other institutions engaged in neural network

research and development.

JPL 94-8, page 25

Part2: NeuralNetworks

Table 1. Comparisonof architecturesand technologies

System Accuracy Speed Technology(bits) ps/conn

AnalogCMOS

ANNA (AT&T) 6 1 0.9#" CMOSDuong et al (JPL) 6 0.5 2#" CMOSKub et al (NRL) 6 0.5 3#" CMOS

CCDs

Chaing (MIT) 6 0.6 3#" CCDOptoelectronic

Frye et al (AT&T) 6 0.5 Si:HDigital

Uchimuri et al (UNM) 8 0.1 0.8#' CMOSNewell et al (NTT) 8 0.025 1.6#" CMOSCID (Caltech) 6 0.6 2#" CMOS

We have implemented both feedback and feedforward architectures using the cascadable

synaptic and neuron building blocks. The computing speed of such systems exceeds 10 9 analog

operations per second. This is an order of magnitude higher than speeds achievable by neuralnet simulations on sequential machines. Using these networks, we have demonstrated content-

addressable, associative memory, terrain trafticability determination, and solutions to the color

graph optimization and Hopfield-Tank traveling salesman problems. This work is currently

leading to the development of application-specific neuroprocessors.

At JPL, we have successfully demonstrated not only the feasibility of hardware

implementations of neural networks, but also--in spite of the inherent, unavoidable precision

limits and noise constraints--unique strengths of analog processing implemented in parallelhardware.

Conclusions

, Massively parallel information processing schemes, inspired by neural network models,

have become a subject of great interest in recent years. Mathematical modeling and

computer simulations have shown emergent computational properties of complex

networks of neuron-like nonlinear processing elements. These networks capture certain

important aspects of intelligent information processing, not easily dealt with by existing

digital and artificial intelligence (AI) technologies.

. Neural network research has matured greatly, thanks to: (a) development of advanced

mathematical theories and new computer tools, and also (b) a better understanding ofneurobiology.

JPL 94-8, page 26


. Artificial neural networks promise efficient solutions to a variety of problems such as

associative, fault-tolerant, information processing, pattern recognition, control, and

computation intensive global optimization operations. They also provide new capabilities,

such as "learning" from experience in the field, self-organization, and generalization, to

solve ill-posed problems.

. Neural networks are an especially valuable technology when the availability of a good

solution in a very short time is more important than its absolute accuracy.

. To date, a large portion of the work in the field is based primarily on software simulation

of the network architectures on standard sequential computers. Undoubtedly, a simulation

of even a moderately large network, with just a few hundred neurons, becomes a

computation-intensive and time-consuming task on a sequential machine. To realize the

potential speed in artificial, inherently parallel, neural network architectures, the neurons

must process information in parallel.

. Today's computer tools--with simulation capabilities of roughly 10 7 interconnects per

second--fall far short of the computational capabilities of even modest biological

networks; a fly, for instance, computes at 10 9 interconnects per second.

. Under the sponsorship of the Defense Advanced Research Projects Agency (DARPA),

and its successor the Advanced Research Projects Agency (ARPA), JPL has focussed on

the development and demonstration of feasibility of fully parallel neural network

architectures. These are used as high speed research tools to study the emergent

properties of neural networks.

, Neural network technology readiness at JPL has already progressed from feasibility

demonstrations to development and rapid hardware prototyping. Stand-alone application-

specific algorithms and coprocessor systems offering real-time functional capabilities,

previously nonexistent, are now available. These tools offer orders-of-magnitude speed

enhancement in computation intensive problems of interest.

JPL 94-8, page 27

PART 3. APPLICATION

HE OPERATION of an electric power system has two objectives: firstly security, secondlyeconomic operation. First, it is necessary to ensure that there is enough generation and

transmission capacity to meet the load. Then, if there is sufficient capacity, the most efficient

way to meet that load can be sought. System operation can be viewed as controlling a multi-

variable system within the constraints of secure operation. In a multidimensional space

representation, the constraints are the boundaries of the space. The system operates at a point

within (or on the boundary of) the space. More flexibility of operation would result from

expanding the boundaries. Such additional flexibility would allow the freedom to improve

efficiency. The object of the work in neural networks is to facilitate energy efficiency by pushing

against the boundaries of secure operation.

In a power network, power flows will distribute themselves in the system according to

Kirchoff's laws. The self-adjusting nature of the system means that the constraints that represent

safe practice may be violated if part of the system changes (for example, because of a fault).

This topic was reviewed in the first part of this report. The practical result is that the system

must be carefully monitored and controlled.

Human operators, trained and experienced, are adept at operating even complicated

power systems. This is the more impressive when one realizes the complexity and magnitude

of the problem. However, no operator can control a system during a disturbance, or in the

seconds following one. The actions of the operator are limited to ensuring that constraints are

JPL 94-8, page 29

PitlDIk_ PAGE BLANt_ NOT FILP,_E,'3

Part 3: Application

not violated during normal operation, and to restoring as much of the system as possible, after

a fault--and the ensuing actions of the protection system--have changed the system config-

uration. Nor can an operator cope with the swings that some systems experience because of

devices that are installed to make possible the transmission of greater amounts of power over

existing rights of way. The problem will be illustrated by means of the example of power systemstabilizers.

The equations that govern the motion of a power system are second-order and non-linear.

The fact that the equations are second order is of no great import, but the nonlinearity reflects

the fact that the system can become unstable. Consider the system of Figure 3-1.

Figure 3-1.Simple power system

GENERATOR

INFINITE

BUS

For a simple power system, such as the one shown in Figure 3-1, consisting of only one gener-

ator and an infinite bus, the motion is described by the swing equation:

M dz6 + em,_ sin5 =Poutdt 2

where M is the inertia constant, a term related to the angular momentum of the generator, 5 is

the angle between the voltages 1"i and 1,'2 at the generator and the bus, X is the impedance of the

generator, or more generally the impedance across which power is transferred, and Pi, is the

shaft input power.

Several simplifying assumptions have been made, particularly with regard to the

constancy of the parameters. The angular momentum of the generator is a function of the speed.

Clearly this is not constant during a swing. The generator impedance is not constant, either,

since the rotor moves relative to the rotating magnetic field of the stator. It is also assumed that

there is no exciter action, that is, the voltage behind the generator impedance is assumed

constant. (In practice, this voltage is controlled by an AVR, as discussed in Section 1.) Never-

theless, in spite of these assumptions, the swing equation is instructive for the purposes of

illustrating the behavior of the system.

This equation is basically a nonlinear version of the equation that describes the motion

of a pendulum. The oscillations typically have a frequency in the order of a second or so,

determined by the inertia of the generator and the impedance of both the generator and the line

between the generator and the bus. The oscillations are not highly damped (there is no first-order

term, because the resistances have been neglected), and can sometimes lead to instability.

The equation also shows that there is a maximum value to the amount of power that can

be transmitted from the generator to the load. This occurs when 5 reaches 90 °. Any further

increase in the power will result in instability.

In practice, systems with long lines are more prone to instability problems, because of

the relatively large value of the transfer impedance. Some improvement can be made by adding

JPL 94-8, page 30

Part 3: Application

capacitors in series with the line. However, this can affect the ability of the system to maintain

a proper voltage profile, and can sometimes lead to subsynchronous oscillations (ie, oscillations

at frequencies less than power frequency), that can be damaging to generators. The instability

problems are characterized by a frequency in the order of 1 Hz, a frequency which is much too

fast for the generator governor to control. (Governor actuation involves moving a large, slow

valve in the steam or water line driving the turbine.)

To guard against this kind of stability problem, it is possible to modulate the signal at

the AVR controlling the generator exciter. This is done by means of a control system called a

power system stabilizer (PSS). In essence, a PSS functions by adding a derivative term to the

equation of motion. It does this by modulating the exciter in response to changes in the power

system. Power system stabilizers represent a relatively new technology, but one that may have

its roots in some work done by the U.S. Bureau of Reclamation in the late 1960s (Schleif and

White, 1966; Schleif, Hunkins, Hattan and Gish, 1969).

Figure 3-2 shows some of the control systems associated with a generator, including a

power system stabilizer.

{ GOVERNORI- SPEED

Figure 3-2.Generator controls

POWER

bOLT L I EXCITER I /_ VOLTAGE

I &AVR _+ REFERENCE

II I _ SPEED ORSTABILIZER I- FREQUENCY

OR POWER

For the application of a PSS to be successful, it must be "tuned" to the power system, that is,

the parameters of the control system must be adjusted so that the modulation has the desired

effect. Gains and frequency responses must be set to the appropriate values. Typically, a

stabilizer will take the derivative of a speed signal, a process which is inherently noisy. To

remove this noise, it will use a low-pass filter. Tuning thus becomes a problem of adjusting the

lead and lag components of the filter in the stabilizer so that the appropriate correcting signal

is available, without noise.

However, the parameters of the power system are not constant, being subject to daily,

weekly and annual cycles, as well as the changes due to the occurrence and clearing of faults.

PSS settings are rarely correct, therefore, long after the original settings have been made.

They suffer from another defect, too. When there is one machine and an infinite bus, it

is easy to see in which direction the modulation must occur to improve the system stability. This

is not so obvious when the power system becomes more complex. Consider the relatively simple

3-machine system of Figure 3-3.

JPL 94-8, page 31

Part 3: Application

Figure3-3.3-machinepower system

In the Figure, three generators supply load to two buses. (One of the generators has no local

load.) Suppose that a PSS is installed on one of the generators, and that the system is disturbed

in some way. The PSS has been tuned for the situation shown, and will act so as to damp the

swing of the machine to which it is attached. Note that the PSS tuning will not be correct if the

system configuration changes. It is fortunate that PSS tuning is relatively "low Q."

Now suppose that a PSS is added to another generator. Interaction between the two

control systems is inevitable. Just as a swing in one part of the system will affect the other parts

of the system, so an action by a PSS in one part of the network will affect the other parts. This

has not been a significant problem in the past because of the low penetration of PSSs into the

power transmission system. However, power system stabilizers are increasingly likely to be seen

as inexpensive alternatives to system reinforcements. Their impact on the power system will

increase. Before long, PSS interactions will be a problem.

Application of Neural Networks

Artificial neural networks mimic the intelligent information processing abilities of the brain. This

is accomplished through a massively parallel architecture containing a number of logic elements

(the biological term is neurons, but the word node is sometimes used), connected to each other

with variable strengths through a large network of interconnections (synapses).

Collectively, neurons with simple properties can accomplish complex functions such as

control, pattern classification, information reconstruction, and learning. Their strength for many

applications arises from their ability to learn and abstract spatial and/or temporal invariances of

mappings. These networks can be built in hardware, or simulated in software.

A solution to the problems of power system stability control based on the use of artificial

neural networks would have wide applicability; as well as being useful as adjuncts to power

system stabilizers, they could be used for control in systems containing dc links, for example,

and systems containing FACTS devices. (FACTS stands for flexible ac transmission system. The

flexibility comes from the use of devices based on solid state switching to control the apparent

value of system parameters by changing the relationship between voltage and current.)

Implemented as an adjunct to a power system stabilizer, a neural net solution might be

as shown in Figure 3-4. Other forms of implementation are possible. In Figure 3-4 the neural

network is essentially an add-on to the stabilizer. In a fully developed system, there may be no

need for the stabilizer to exist separately from the neural network. All the functions of the

stabilizer could be implemented in the network.

JPL 94-8, page 32

Part 3: Application

I GOVERNOR I "

SPEED

Figure 3-4.Power system stabilizerwith neural network

POWER

L._ I K.........)1_ | VOLTAGE

- _ _ S.IGNALI EXC ERI _AVR I--_+ VOLTAGE

REFERENCE

I STABILIZER I. _ SPEEDVOLTAGE

NEURALPARAMETER NETWORK

VALUES _._.ENT

An advantage of the implementation shown in Figure 3-4 is that the stabilizer works without the

need to choose the input parameter (speed, frequency or power) in advance. The neural network

can make this choice in real time, probably as some kind of optimal blend of parameters. The

exact blend would depend on the particular system disturbance, so that the system performance

should be better than a conventional stabilizer. Other advantages include the possibility of

training the system off-line in advance of installation, and the abi/ity of the stabilizing function

to track system changes in the years that follow initial installation.

At present there are relatively few systems with dc links, and these tend to be large links

installed primarily for the transfer of large amounts of power over long distances. A major

example of this is the Pacific Intertie, an arrangement of two ac lines and one dc line that brings

power from the predominantly hydro resources of the Pacific Northwest to southern California.

It is pointed out that the power flow on the dc line is modulated so as to improve the stability

of the underlying ac system.

If dc links become more common--and this is thought to be a thrust of other research

being funded by DOE--interaction could be avoided simply by not modulating the power flow

in response to conditions in the ac system. However, this would be failing to take advantage of

an opportunity to use the system more efficiently, and the cost could be very large. Modulation

should be considered from the outset. A complex system of multiple controllable dc links would

be an ideal candidate for neural net operation.

FACTS devices were designed to be modulated. The paradigm is the variable capacitor,

designed to be used in series with a long transmission line. The FACTS device would enable the

apparent value of the line impedance to be modulated; essentially varying X in Figure 3-1. It is

understood how the modulation signal for a FACTS device should be derived. It is not under-

stood what to do when there are multiple devices.

JPL 94-8, page 33

Part 3: Application

Future Work: Feasibility Study and Network Selection

The application of artificial neural networks to power system stability is motivated by the fact

that neural networks are self-programmable computational tools. A net may be comprised of

dozens or hundreds of simple processors that, like brain neurons, can receive and send signals

to many others. The weights of the various connections (W_j in Figure 2-1) can be changed by

training. The network changes its dynamic structure as a result of learning from its own

"experience." One fascinating--and suggestive--aspect of neural nets is that their inner

workings are not directly controlled, or even accessible. The network has "emergent" properties:

that is it can exhibit new behavior by creating new combinations of pre-existing elements.

Various groups of AI researchers have concentrated on particular implementations of

neural networks, and particular ways of training the nets. At the California Institute of

Technology, an interconnected network that functions as a content-addressable memory was

developed by Professor J.J. Hopfield. Weights are downloaded. Other multi-layer networks can

be trained by "back-propagation," which functions much like negative feedback. A two-layer

network first described by Professor T. Kohonen in 1982 is trained without supervision. Theessential difference between the various networks is whether there are constraints on the

permissible weights that, for example, prohibit or encourage lateral connection of neurons, or

prohibit the backward flow of information in the network. For the time being, consider the

neural network to be a perfectly general network, in which any neuron is permitted a connection

to any other.

Neural nets have much to offer over conventional computers. They can be faster and

more robust, because of the parallel and distributed nature of the computation. They can also

generalize, and respond accurately to situations that they have not seen before. It is this aspect

of neural nets that makes them particularly attractive in many applications.

The work on power system application of artificial neural networks on the Communi-

cations and Control Project began in 1992, with a study of the feasibility of using neural nets

to solve the problem of security assessment in power systems. While this study is not complete

at the time of writing this document, the work has shown that the Kohonen net can indeed solve

the security assessment problem. The present work is under way to examine the feasibility of

using a neural network to perform active stability control. It can be assumed that neural nets will

be shown to be a valid solution to the problem of the control of the large nonlinear power

system. This being the case, the next step will be to build on this foundation by determining

what kind of network offers most promise. Whatever the specific neural architecture finally

selected for this particular application, the network can be made to learn to identify the behavior

of the power system by changing the synaptic interconnections incrementally and recursively

until all possible behaviors are learned. The trained neural networks will be tested and evaluated

by presenting to it data from the training library as well as new data.

By mid-1994, the feasibility of using a neural net solution to address the problems of

controlling the stability of the power system should have been demonstrated theoretically. The

choice of which network type to use will likely also have been made. At this point, if it has not

already been secured, industrial cofunding for the work will be sought. In collaboration with

DOE and an industry co-sponsor, it will be decided whether a neural controller should be

developed for FACTS devices, PSSs, or for dc links.

JPL 94-8, page 34

Part 3: Application

Once the decision to address a particular subset of the problem is made, the proposed

solution can be tested by simulation. This will certainly be a software simulation at first, and

will require development of simulation code for the network and analysis software for the power

system. At first, it will be appropriate to use a simplified model for the power system, consisting

of a few buses and containing some simplifying assumptions. Once the neural network model

has been shown to be capable of controlling such a system, a more complete model must beused.

A power system analysis package would be an ideal candidate for a realistic test of the

neural network solution. To perform such a test, the neural net simulation program and the

power system transient stability program will have to be integrated, itself no trivial task.

A further step towards realizing neural net control of power system stability would be

to implement the neural network in hardware, possibly by means of digital signal processing,

and to connect the hardware to a real power system. This work would require a careful, phased

implementation approach, and it is unlikely it could begin until 1995 at the earliest.

JPL 94-8, page 35

APPENDIX A. NEURAL LEARNING FORMALISM

E FORMALIZE a neural network as an adaptive dynamical system whose temporalevolution is governed by the following set of coupled nonlinear differential equations:

.,, + K,,u,, = g,,(%,(_.., T.,,,u,,,+I,,)) t > 0 (A-l)

where u. represents the output of the n `h neuron, (u. (0) being the initial state). T.,. denotes the

strength of the synaptic coupling from the m th to the n th neuron. The constants x characterize the

decay of neuron activities. The sigmoidal functions g.(e) modulate the neural responses, with

gain given by 3'., typically, g.(x) = tanh(_/2c). To implement a nonlinear functional mapping

from an Ncdimensional input space to an No-dimensional output space, the neural network is

topographically partitioned into three mutually exclusive regions. As shown in Figure A-l, the

partition refers to a set of input neurons Sx, a set of output neurons So, and a set of "hidden"

neurons Sn. Note that this architecture is not formulated in terms of "layers", and that each

neuron may be connected to all others including itself. To specify the term I. we distinguishbetween two different cases:

PAGE BLAi"_ NOT FILMED

JPL 94-8, page 37

Appendix A. Neural Learning Formalism

Input set, S i Output set, S o/

Figure A- 1.

Topology of a°=general networkE

0.

"50

0

0Z

Case 1: A temporal pattern is presented to the network. In which case, a(t) (henceforth the

bold font will denote a vector) is a N-dimensional vector of target temporal patterns, with

non zero elements, a.(t), in the input and output sets only. When trajectories, rather than

mappings, are considered, components in the input set may also vanish. Hence, the time-

dependent external input term in Eq. (A-l), ie I_(t), encodes the component contribution

of the target temporal pattern via the expression

a.(t) if neS t/.(0= 0 if n eSMU S o(A-2)

To proceed formally with the development of a temporal learning algorithm, we consider

an approach based upon the minimization of an error functional, E, defined over the time

interval [t o, tl] by the following expression

1 y

E( u,p ) = -__o _ e 2.dt = ,_,otiFdt (A-3)

where the error component, e.(t), represents the difference between the desired and actual

value of the output neurons, ie

if n_ S O (A-4)

if ne SzUS n

Case 2: Static patterns are presented to the network, in which case, the "source" term I k

encodes the contribution of the ]#h training sample via the following expression:

ik={ ak. if neS 10 if neSnUS o

(A-5)

JPL 94-8, page 38


As in the temporal case, the development of a static supervised learning algorithm

requires minimization of an error function, E, given by the following expression:

2 k n_(ti#- a#) 2 VnqStUS o(A-6)

Where the vector a denotes the steady state solution of the neural activation dynamics,

Eq.(A-1).

In both static and temporal models, the internal dynamical parameters of interest are the

strengths of the synaptic interconnections, T,_, the characteristic decay constants, r., and the

gain parameters, q,n. They can be presented as a vector of M (M = N 2 + 2N) components:

(A-7)P = [Tll, "", TNN' KI' ""'KN_YI' ""' YN]

We will assume that elements of p are statistically independent. Furthermore, we will also

assume that, for a specific choice of parameters and set of initial conditions, a unique solution

of Eq. (A-l) exists. Hence, the state variables u are an implicit function of the parameters p.

In the rest of this document, we will denote the #th element of the vector p by p, (# = 1,-.-,

M) and limit ourselves to the temporal learning case due to its importance to our application.

Traditionally, learning algorithms are constructed by invoking Lyapunov stability

arguments, ie by requiring that the error functional be monotonically decreasing during the

learning time, 7". This translates into

dE__ dE dp_de .=, < 0

(A-8)

One can always choose, with 71 > 0

dp. _ dErl (A-9)

dr. dp,

which implements learning in an inherently local minimization procedure. Attention should be

paid to the fact that Eqs. (A-I) and (A-9) may operate on different time scales, with parameter

adaptation occurring at a slower pace. Integrating the dynamical system, Eq.(A-9), over the

interval [r, T+A_'], one obtains

p.('c +Ar.) = p_,(r.)-rl f _÷_ dE dz, (A-10)" "_ dp p.

JPL 94-8, page 39


Equation (A-10) implies that, in order to update a system parameter p_, one must evaluate the

"sensitivity" (ie, the gradient) of E, Eq. (A-3), with respect to p_ in the interval [r, r+Ar].

Furthermore, using Eq. (A-3) and observing that the time integral and derivative with respect

to p, commute, one can write

de _ f,: f,,Or. O.=f': m . --mato :,o Op :,o ,gu Op.

(A-11)

This sensitivity expression has two parts. The first term in the right hand side of Eq.(A-11) is

called the "direct effect", and corresponds to the explicit dependence of the error functional on

the system parameters. The second term in the right hand side of Eq. (A-11) is called the

"indirect effect", and corresponds to the implicit relationship between the error functional and

the system parameters via u. In our learning formalism, the error functional, as defined by

Eq. (A-3), does not depend explicitly on the system parameters; therefore, the "direct effect"

vanishes, ie

aF-0

0p_, (A-121

Since F is known analytically (namely, Eqs. (A-3) and (A-4)), computation of aF/Ou is straight-forward. Indeed

OF- e (A-13)

OU n n

Thus, to enable evaluation of the error gradient using Eq. (A-11), the "indirect effect" matrix

Ou/Op should, in principle, be computed.

In summary, the problem of temporal learning is typically formulated as a minimization,

over an arbitrary but finite interval, of an appropriate error functional. The gradients of the

functional with respect to the various parameters of the neural architecture, eg synaptic weights,

neural gains etc, are essential elements of the minimization process. In the past, major efforts

have been devoted to the efficacy of their computation.

Calculating the gradients of a system's output with respect to different parameters of the

system is, in general, of relevance to several disciplines. Hence, a variety of methods have been

proposed in the literature for computing such gradients. We will briefly mention only thosewhich are relevant to our work.

Williams and Zipser (1989) presented a scheme in which the gradients of an error

functional with respect to network parameters are calculated by direct differentiation of the

neural activation dynamics. This approach is computationally very expensive and scales poorly

to large systems. The inherent advantage of the scheme is the small storage capacity required,

which scales as O(N3), where N denotes the size of the network.

Pearlmutter (1989), on the other hand, described a variational method which yields a set

JPL 94-8, page 40


of linear ordinary differential equations for backpropagating the error through the system. These

equations, however, need to be solved backwards in time. It requires temporal storage of

variables from the network activation dynamics, thereby reducing the attractiveness of the

algorithm.

Recently, Toomarian and Barhen (1992) suggested an approach for calculating the

gradients of an error functional with respect to the system's parameters. It builds upon advances

in nonlinear sensitivity theory. In particular, it exploits the concept of adjoint operators to reduce

the computational costs. Two novel systems of equations for error propagation (ie, the adjoint

equations), are at the heart of our computational framework. These equations are solved

simultaneously (ie, forward in time) with the network dynamics. The computational complexity

of the algorithm scales as O(N 3) per time step. The storage requirements are minimal ie, of the

order of O(N2).

JPL 94-8, page 41

REFERENCES

Aleksander, I. (Ed.) (1989). Neural Computing Architectures: The Design of Brain Like

Machines, Cambridge, MA: The MIT Press.

Amari, S. I. (1972). Characteristics of Random Nets of Analog Neuron-Like Elements, IEEE

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Amari, S. I. (1979). A Neural Theory of Association and Concept Formation, Bio. Cyber., 26,

175-185.

Amari, S.-I. (1983). Field Theory of Self-organizing Neural Networks, IEEE Trans. Sys., Man,

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Carpenter, G.A. & Grossberg S. (1987a). A Massively Parallel Architecture for a Self-

Organizing Neural Pattern Recognition Machine, Comp. Vis., Gra., and Image Proc.,

37, 54-115.

Carpenter, G.A. & Grossberg, S. (1987b). ART 2: Self-Organization of Stable Category

Recognition Codes for Analog Input Patterns, Applied Optics, 26(23), 4919-4930.

Elgerd, O.I. (1971). Electric Energy Systems Theory: An Introduction, New York: McGraw-Hill.

Graubard, S.R. (1989). The Artificial Intelligence Debate: False Starts, Real Foundation,

Cambridge, MA: The MIT Press.

Grossberg, S. (1987a). The Adaptive Brain, I: Cognition, Learning, Reinforcement and Rhythm,Amsterdam: Elsevier/North-Holland.

Grossberg, S. (1987b). The Adaptive Brain, H: Vision, Speech, Language and Motor-Control,Amsterdam: Elsevier/North-Holland.

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olt_ll_',_ PAGE IB!.$d',_3(I'#OT F|L:'-".'Zt_

References

Grossberg, S. (1988). Nonlinear Neural Networks: Principles, Mechanisms, and Architectures,

Neural Networks, 1(1), 17-62.

Hebb, D.O. (1949). Organization of Behavior, New York, NY: John Wiley.

Hofstader, D.R. (1979). G6del, Escher, and Bach, New York, NY: Bantam Books.

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JPL 94-8, page 45

TECHNICAL REPORT STANDARD TITLE PAGE,, | i,,

l. Report No. 94-8 1 2. Government..,, Accession No. 3. Reclplent's Catalog No.

4. Title and Subtitle

COMMUNICATION AND CONTROL FOR ELECTRIC POWER SYSTEMSPOWER SYSTEM STABILITY APPLICATIONS OF ARTIFICIAL

5. Report DateApril 1994

6. Performing Organization Code

8. Performing Organization Report No.

NEURAL NETWORKS

7. Author_) N. Toomarian

H. Kirkham

9. Per_rming Organization Name and Address

JET PROPULSION LABORATORY

California Institute of Technology4800 Oak Grove Drive

Pasadena, California 91109

"12. Sponsoring Agency Name and Addres_

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Washington, D.C. 20546i, • ii

15. Supplementary Notes

94-810. Work Unlt No.

11. Contract or Grant No.NAST-918

1'3: Type of Report and Period Covered

Final Report

14. Sponsoring Agency Code

16. Abstract

This report investigates the application of artificial neural networks to the

problem of power system stability. The field of artificial intelligence, expertsystems and neural networks is reviewed. Power system operation is discussed with

emphasis on stability considerations. Real-time system control has only recently

been considered as applicable to stability, using conventional control methods.The report considers the use of artificial neural networks to improve the stability

of the power system. The networks are considered as adjuncts and as replacements

for existing controllers. The optimal kind of network to use as an adjunct to a

generator exciter is discussed.

17. Key Wor_ _elected by Author_))Artificial Neural Networks

Power System Control

Power System Stability

Artificial Intelligence

Expert Systems

19. Security Cl_slf. _f'thls repot)

18.'Distrlbution Statement

20. Security Classif. (of thls page) 21. No. of Pages

4S

PAGE li_.AN'R I',K)T FtLI_'Ur-?

22. Price

JPt_ 0184, R _1_

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